Please explain step by step solution and derivations. Explain your logic behind equations choice. Thabk you.

Water$-$vapor mixture flows through a long pipe at an average temperature of $T=100C.$ The inner and outer radili of the pipe are $r_1=6cm$ and $r_2=6\mathrm{.}5cm,$ respectively. The outer surface of the pipe is wrapped with a thin electric heater that consumes $300$ W per $m$ length of the pipe. The exposed surface of the heater is heavily insulated so that the entire heat generated in the heater is transferred to the pipe. The temperature of the inner surface and water$-$vapor minture is maintained at $100$ C by evaporation of the liquid. The thermal conductivity of the pipe material is $16\frac{W}{m}K.$ Find out temperature distribution T$($r$)$ in the pipe wall. Calculate heat flux and heat flow at $r=6cm$ and $6\mathrm{.}2$ cm $,$ respectively, is the heat flux constant? Is heat flow $($per init length of the pipe$)$ constant in the radial direction?

$(1)1$D$,$ steady state, constant material properties, zero heat generation,

$(2)$ Solution based on unit lenegth of $1=1m$

$(3)$ Governing equation: $\frac{3}{r}d(krr\frac{d}{d})=0$